Barcode entropy and relative symplectic cohomology

2026/01/22 by Jonghyeon Ahn · 1 voice · 1 citation
Mathematics · #math.SG

paper · pdf

Abstract

In this paper, we study the barcode entropy--the exponential growth rate of the number of not-too-short bars--of the persistence module associated with the relative symplectic cohomology SH_M(K) of a Liouville domain K embedded in a symplectic manifold M. Our main result establishes a quantitative link between this Floer-theoretic invariant and the dynamics of the Reeb flow on ∂ K. More precisely, we show that the barcode entropy of the relative symplectic cohomology SH_M(K) is bounded above by a constant multiple of the topological entropy of the Reeb flow on the boundary of the domain, where the constant depends on the embedding of K into M.

Citations

• Comparison of symplectic capacities
• Wrapped Floer homology and hyperbolic sets
• Barcode entropy and wrapped Floer homology
• S¹-equivariant relative symplectic cohomology and relative symplectic capacities
• On the barcode entropy of Lagrangian submanifolds
• On the Barcode Entropy of Reeb Flows
• Invariant Sets and Hyperbolic Closed Reeb Orbits
• Topological entropy of Hamiltonian diffeomorphisms: a persistence homology and Floer theory perspective
• Symplectic topology and ideal-valued measures
• Topological Persistence in Geometry and Analysis
• Symplectic homology and the Eilenberg-Steenrod axioms
• Contact homology and virtual fundamental cycles
• Persistent homology and Floer-Novikov theory
• Autonomous Hamiltonian flows, Hofer's geometry and persistence modules
• The structure and stability of persistence modules
• Morse theory for periodic solutions of hamiltonian systems and the maslov index

Cited by

• A lower bound for relative symplectic cohomology barcode entropy

Discussions

• Jonghyeon Ahn: Barcode entropy and relative symplectic cohomology https://arxiv.org/abs/2601.15606 https://arxiv.org/pdf/2601.15606 https://arxiv.org/html/2601.15606 [bsky, 0 points, 0 comments]

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